Whakaoti i te 100x^2+8x+6*3^2=583.3

$$100 x ^ { 2 } + 8 x + 6 \cdot 3 ^ { 2 } = 583.3$$

Whakaoti mō x

$$x=\frac{\sqrt{52946}}{100}-0.04\approx 2.260999783$$

$$x=-\frac{\sqrt{52946}}{100}-0.04\approx -2.340999783$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

$$100x^{2}+8x+6\times 9=583.3$$

Whakareatia te 6 ki te 9, ka 54.

$$100x^{2}+8x+54=583.3$$

Tangohia te 583.3 mai i ngā taha e rua.

$$100x^{2}+8x+54-583.3=0$$

Tangohia te 583.3 i te 54, ka -529.3.

$$100x^{2}+8x-529.3=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 100 mō a, 8 mō b, me -529.3 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8±\sqrt{8^{2}-4\times 100\left(-529.3\right)}}{2\times 100}$$

Pūrua 8.

$$x=\frac{-8±\sqrt{64-4\times 100\left(-529.3\right)}}{2\times 100}$$

Whakareatia -4 ki te 100.

$$x=\frac{-8±\sqrt{64-400\left(-529.3\right)}}{2\times 100}$$

Whakareatia -400 ki te -529.3.

$$x=\frac{-8±\sqrt{64+211720}}{2\times 100}$$

Tāpiri 64 ki te 211720.

$$x=\frac{-8±\sqrt{211784}}{2\times 100}$$

Tuhia te pūtakerua o te 211784.

$$x=\frac{-8±2\sqrt{52946}}{2\times 100}$$

Whakareatia 2 ki te 100.

$$x=\frac{-8±2\sqrt{52946}}{200}$$

Nā, me whakaoti te whārite x=\frac{-8±2\sqrt{52946}}{200} ina he tāpiri te ±. Tāpiri -8 ki te 2\sqrt{52946}.

$$x=\frac{2\sqrt{52946}-8}{200}$$

Whakawehe -8+2\sqrt{52946} ki te 200.

$$x=\frac{\sqrt{52946}}{100}-\frac{1}{25}$$

Nā, me whakaoti te whārite x=\frac{-8±2\sqrt{52946}}{200} ina he tango te ±. Tango 2\sqrt{52946} mai i -8.

$$x=\frac{-2\sqrt{52946}-8}{200}$$

Whakawehe -8-2\sqrt{52946} ki te 200.

$$x=-\frac{\sqrt{52946}}{100}-\frac{1}{25}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{52946}}{100}-\frac{1}{25} x=-\frac{\sqrt{52946}}{100}-\frac{1}{25}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

$$100x^{2}+8x+6\times 9=583.3$$

Whakareatia te 6 ki te 9, ka 54.

$$100x^{2}+8x+54=583.3$$

Tangohia te 54 mai i ngā taha e rua.

$$100x^{2}+8x=583.3-54$$

Tangohia te 54 i te 583.3, ka 529.3.

$$100x^{2}+8x=529.3$$

Whakawehea ngā taha e rua ki te 100.

$$\frac{100x^{2}+8x}{100}=\frac{529.3}{100}$$

Mā te whakawehe ki te 100 ka wetekia te whakareanga ki te 100.

$$x^{2}+\frac{8}{100}x=\frac{529.3}{100}$$

Whakahekea te hautanga \frac{8}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x^{2}+\frac{2}{25}x=\frac{529.3}{100}$$

Whakawehe 529.3 ki te 100.

$$x^{2}+\frac{2}{25}x=5.293$$

Whakawehea te \frac{2}{25}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{1}{25}. Nā, tāpiria te pūrua o te \frac{1}{25} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{2}{25}x+\left(\frac{1}{25}\right)^{2}=5.293+\left(\frac{1}{25}\right)^{2}$$

Pūruatia \frac{1}{25} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{2}{25}x+\frac{1}{625}=5.293+\frac{1}{625}$$

Tāpiri 5.293 ki te \frac{1}{625} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x^{2}+\frac{2}{25}x+\frac{1}{625}=\frac{26473}{5000}$$

Tauwehea x^{2}+\frac{2}{25}x+\frac{1}{625}. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{1}{25}\right)^{2}=\frac{26473}{5000}$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$\sqrt{\left(x+\frac{1}{25}\right)^{2}}=\sqrt{\frac{26473}{5000}}$$

Whakarūnātia.

$$x+\frac{1}{25}=\frac{\sqrt{52946}}{100} x+\frac{1}{25}=-\frac{\sqrt{52946}}{100}$$

Me tango \frac{1}{25} mai i ngā taha e rua o te whārite.

$$x=\frac{\sqrt{52946}}{100}-\frac{1}{25} x=-\frac{\sqrt{52946}}{100}-\frac{1}{25}$$